Finite Group DatabasebetaFinite Group Databasebeta| order | 11780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D589 |
| unambiguous semidirect product | (D5×C19)⋊D31 |
| unambiguous semidirect product | (D5×C31)⋊D19 |
| Fitting, socle, derived, Hall | C5×C19×C31 ⋊ C22 |
| Hall | C19×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×D19 |
| Hall | C5×C19 ⋊ C2×D31 |
| Sylow | C31 ⋊ D5×D19 |
| Sylow | C19 ⋊ D5×D31 |
| Sylow | C5 ⋊ C2×D589 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C19×C31 | C22 |
| LCS | G ▷ C5×C19×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×#16812976, D5×#16812975, D5×(C19⋊C3)⋊D31, … |
| maximal normal subgroup of | D5×#16812976, D5×#16812975, D5×(C19⋊C3)⋊D31, … |
| maximal quotient of | C3×D5×D589, D15×D589, D5×D1767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11780, 28);